Hi, I have some issues with the bottom phalanges of my right hand (the small ones, that is the nearest to the tip of the fingers). I'm from Argentina so English is not my native, I apologize for any grammatical or spelling mistake.

So, when a finger of the right hand impacts against a string, when using "tirando", the phalanges always bends. In this photo I show the right moment when the problem occurs:

I've been studying for 5-6 years now in a conservatoire here and always had that problem, only one professor noticed that problem. He commented me that he had that problem and the principal consequences of it was that the right hand would lack of the right strenght and speed, this week I'm going to take classes with him to try to solve it. But in case it does not work properly I was wondering if anyone here had that problem.

I also noticed it is a somehow weird condition, i asked many fellow guitarist to show me their tirando technique and their phalanges practically don't move, so they don't have that problem. I also asked non-guitarist to try the tirando, and surprise, they don't have that issue either.

I tried anticipation excercises (again, I'm from Argentina, I don't know how you would call them), that would be: playing open strings with staccato and as soon as a finger attacks a string, the next one must be positioned instantly on the same string producing the staccato. It's an excercise a Matteo Carcassi specialist suggested me (he also suggested me to try the Carcassi treatise on guitar which didn't solve the problem).

I always try to trigger the movement of the fingers of the right hand by moving only the upper phalanges of it, but still the bottom phalanges bend.

From the picture, it appears that you have hyper mobile finger joints. This means that they can bend backwards if you relax your muscles.
I have the same condition.
My middle finger joints are even *more* mobile than the tip joints. If I strongly extend my fingers, you would see an arc that places my fingertips well above the back of my hand.
This is not a fatal flaw, so don't worry! I can play guitar and choose how much to allow the tip to collapse to get the exact sound I am after.
Here is how I learned to do it.
When you practice tirando, think of that end joint as having a micro bend in the flexed direction in it as you contact the string. If it starts to collapse, think of it having a bit more of a bend. If it still starts to collapse, don't push down as hard on the string. You are trying to train a very delicate mechanism and the feedback to control it. You don't want to "harden" your hand, you want to find the exact point of balance needed to control the amount of flex you wish to have. It is all about sensation and careful exploration of your body's response to the forces you are using to play. This is something that you do as an exercise, not while trying to play music. With careful exploration, you will find the exact amount of "micro bend" needed in that joint for the force you are putting on the string and it will be your choice how much bend to allow to get the exact sound you want, then your ear will tell your brain what to do.
The control may be weak in the beginning, but with patient training and full attention to the sensation of that balance point; just enough bend to keep from collapse, you will develop a delicate control of your joint position.

From the picture, it appears that you have hyper mobile finger joints. This means that they can bend backwards if you relax your muscles.
I have the same condition.
My middle finger joints are even *more* mobile than the tip joints. If I strongly extend my fingers, you would see an arc that places my fingertips well above the back of my hand.
This is not a fatal flaw, so don't worry! I can play guitar and choose how much to allow the tip to collapse to get the exact sound I am after.
Here is how I learned to do it.
When you practice tirando, think of that end joint as having a micro bend in the flexed direction in it as you contact the string. If it starts to collapse, think of it having a bit more of a bend. If it still starts to collapse, don't push down as hard on the string. You are trying to train a very delicate mechanism and the feedback to control it. You don't want to "harden" your hand, you want to find the exact point of balance needed to control the amount of flex you wish to have. It is all about sensation and careful exploration of your body's response to the forces you are using to play. This is something that you do as an exercise, not while trying to play music. With careful exploration, you will find the exact amount of "micro bend" needed in that joint for the force you are putting on the string and it will be your choice how much bend to allow to get the exact sound you want, then your ear will tell your brain what to do.
The control may be weak in the beginning, but with patient training and full attention to the sensation of that balance point; just enough bend to keep from collapse, you will develop a delicate control of your joint position.

Very useful information there, however I'm not sure if hypermobility is the condition I have, my hand doesn't look like these ones:

My hand does not look like those pictures, either. However, my fingertip joints can do what yours do, as well as having elbows that can bend beyond merely straight. That is, I was told by my doctor, hypermobile joints. That may have not been the correct diagnosis, nevertheless, the solution to hyperextension, is to teach yourself the fine control that compensates for the extra range of motion you have.

Yes, his tip joints flex a lot. I also looked at his fretting hand and although there were a few moments when those tip joints flexed, for the majority of the time they did not. This indicates to me that it is his choice to allow his right hand joints to flex, not a default because he cannot prevent them from flexing. So a question I would have for the OP would be if he has a problem with tip joint collapse in his left hand or not. The joint mobility is usually the same in both hands (barring injury) and if he wishes to choose when to flex his right hand tips and does not have a problem with the left hand, he has already solved the problem of control once.
It should be a choice, IMO, not a default. I choose how much flex to allow depending on the sound desired. The softer attack with the flexed tip, or a harder edged attack with less flex to get the musical effect I am after.

It also sometimes depends on nail length, especially with my a finger. I allow more flex with that finger if I hear a difference in sound between that note and others played in the melody line...and then I reach for my file!

If you need more reassuring exemples, and in the classical scene, be aware that Ricardo Gallén is precisely using what you see as a problem: a very mobile 1st phalange, the release of the pressure/tension will provide for the sound you want, depending on the amount of pressure/tension, and a quick and automatic/natural return to the original position, which means you will be able to play fast...

Yes, his tip joints flex a lot. I also looked at his fretting hand and although there were a few moments when those tip joints flexed, for the majority of the time they did not. This indicates to me that it is his choice to allow his right hand joints to flex, not a default because he cannot prevent them from flexing. So a question I would have for the OP would be if he has a problem with tip joint collapse in his left hand or not. The joint mobility is usually the same in both hands (barring injury) and if he wishes to choose when to flex his right hand tips and does not have a problem with the left hand, he has already solved the problem of control once.
It should be a choice, IMO, not a default. I choose how much flex to allow depending on the sound desired. The softer attack with the flexed tip, or a harder edged attack with less flex to get the musical effect I am after.

It also sometimes depends on nail length, especially with my a finger. I allow more flex with that finger if I hear a difference in sound between that note and others played in the melody line...and then I reach for my file!

Hi lagartija, well the answer to that varies, most oftenly the tips of the joints of the left hand don't collapse; but If I apply way too much pressure they may bend back.
Also, respecting the Vicente Amigo video, I'm not entirely sure, but I think he's using "apoyando" (I think that's the term in english), not "tirando", which is normal in that technique.. although I hear an arpeggio? Maybe he's plucking his thumb and at the same time he's using "apoyo" in the upper strings. Something like Alirio Diaz' tremolo (he plays tremolo apoyando).

Yes, his tip joints flex a lot. I also looked at his fretting hand and although there were a few moments when those tip joints flexed, for the majority of the time they did not. This indicates to me that it is his choice to allow his right hand joints to flex, not a default because he cannot prevent them from flexing. So a question I would have for the OP would be if he has a problem with tip joint collapse in his left hand or not. The joint mobility is usually the same in both hands (barring injury) and if he wishes to choose when to flex his right hand tips and does not have a problem with the left hand, he has already solved the problem of control once.
It should be a choice, IMO, not a default. I choose how much flex to allow depending on the sound desired. The softer attack with the flexed tip, or a harder edged attack with less flex to get the musical effect I am after.

It also sometimes depends on nail length, especially with my a finger. I allow more flex with that finger if I hear a difference in sound between that note and others played in the melody line...and then I reach for my file!

Hi lagartija, well the answer to that varies, most oftenly the tips of the joints of the left hand don't collapse; but If I apply way too much pressure they may bend back.
Also, respecting the Vicente Amigo video, I'm not entirely sure, but I think he's using "apoyando" (I think that's the term in english), not "tirando", which is normal in that technique.. although I hear an arpeggio? Maybe he's plucking his thumb and at the same time he's using "apoyo" in the upper strings. Something like Alirio Diaz' tremolo (he plays tremolo apoyando).

If the tip joints collapse in your left hand only when you apply "way too much" pressure, it means that you have adjusted the bend in the tip joints to work correctly for "the right amount " of pressure, and the collapse lets you know that you are applying "way too much" and you back off on the pressure. You can train your right hand in the same way. Find out how much bend to use in the tip joints when playing at different volumes to avoid tip collapse. There may be an ultimate limit as there is in your left hand, but more likely it is just the awareness of what you need to do that you need to practice in exercises. Once you find out how much bend to use to keep the joint stable, you can choose the appropriate amount of flexing for what you want to do.
With regard to the video, he uses both apoyando and tirando. His tip joints don't collapse in tirando. I saw him play an arpeggio in the beginning where i was apoyando but m and a were tirando.

Based off the picture from the OP - it looks like part of the problem is you are pushing on the string. I'm not going to rule out the "over extension" that lagartija is speaking of because the control of your range of motion is important to.

However, I'd start off by just putting all of my fingerings on the top 4 strings: P - 4 (or 5), I - 3, M - 2, A - 1. Can you have your fingers on these strings and keep the hand curled? If not, learn to control the pressure and curvature of your fingers so that there is a gentle curl in your fingers when they are on the strings. You should be pushing into or depressing the string (based off the picture - it appears that you are doing that - as the 3rd string is pushed closer to the 4th string than the 2nd string). Start with that, and develop the sensation of "standing on the strings without applying pressure". From there push into the string to play and have the finger(s) return and again relax them to the point of where they keep the shape of a gentle curve.